Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11522 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12806 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #410 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| socle | C2×C19 | #1799 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×C8×C19 ◁ C2×C19×#131 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30)(23,34)(24,37,38,27)(25,29)(26,32)(28,36)(31,45)(33,43,47,44)(35,42,50,49)(39,51,40,48)(41,46);(20,22,23,32,25,31,36,46)(21,26,28,30,29,41,34,45)(24,33,35,48,38,47,50,51)(27,40,42,44,37,39,49,43);(21,27)(22,31)(26,39)(28,42)(29,37)(30,43)(32,46)(33,47)(34,49)(40,41)(44,45)(48,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5794);